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<?xml version="1.0" standalone="yes"?> <Paper uid="P85-1008"> <Title>Ontological Promiscuity</Title> <Section position="4" start_page="0" end_page="83" type="metho"> <SectionTitle> 3 The Logical Notation </SectionTitle> <Paragraph position="0"> Davidson (1967) proposed a treatment of action sentences in which events are treated as individuals. This facilitated the representation of sentences with time and place adverbials. Thus we can view the sentences John ran on Monday.</Paragraph> <Paragraph position="1"> John ran in Sin Fnmciaco.</Paragraph> <Paragraph position="2"> as mmerting the existence of & ruxming event by John and asserting a relation between the event and Monday or San Francisco. We can similarly view the sentence John ran slowly.</Paragraph> <Paragraph position="3"> as expressing an attribute about a running event. Treating events as individuals is abe useful beemme they can be acgumerits of statements about cremes: Because he wanted to get there first, John ran.</Paragraph> <Paragraph position="4"> Because John ran, he arrived sooner than anyone else. They can be the objects of propositional attitudes: Bill was surprised that John ran.</Paragraph> <Paragraph position="5"> Finally, this approach accomodates the facts that events can be nominalized and can be referred to pronominally: John's running tired him out.</Paragraph> <Paragraph position="6"> John ran, and Bill saw it.</Paragraph> <Paragraph position="7"> But virtually every predication that can he made in natural language can be specified u to time and place, be modified adverbially, function a~ a cause or effect of something else, be the object of a propositional attitude, be nominalized, and be referred to by a pronoun. It is therefore convenient to extend Davidson's approach to all predications. That is, corresponding to any predication that can he made in natural lan~tage, we will say there is an event, or state, or condition, or sitl=ation. or &quot;eventuality', or whatever, in the world that it refer~ to. This approach might he called &quot;ontnlogical promiscuity'. 0lie abandons all ontological scruples.</Paragraph> <Paragraph position="8"> Thus we would like to have in our logical notation the possibility of an extra argument in e~h predication referring to the &quot;condition&quot; that exists when that predication is true. However. especially for expository convenience, we would like to retain the option of not specifying that extra argument when it is not needed and would only get in our way. Ilence, I propose a logical notation that provides two sets of predicates fhat are ~ystematically related, by introducing what might I)e railed a &quot;nominalization&quot; operator '. (:orresponding lu every rl-ary predicate p there will he an n + I-ary predicalc i ~t who.~e (i~t argqlnlenl can he thought of a.~ the condilion that }mhl~ '*hen p is rnw of the suhsequent ar~lments. Thus. if r..(J) me,~ns that .John runs, run'(E, J) means that /': is a running event hy ,John. or John's running, if slipperv(F ) means that floor F is slippery, then Jlipperv~(E, F) means that ~&quot; is the condition of F's being slippery, or F's slipperiness. The effect of this notational maneuver is to provide handles by which various predications can be grasped by higher predications. A similar approach haL~ been in many AI systems.</Paragraph> <Paragraph position="9"> In discourse one not only makes predications about such ephemera as events, states and conditions. One also refers to crttities that do not actually exist. Our notation must thus have a way of referring to such entities. We therefore take our model to he a Platonic universe which contains everything that can he spoken of - objects, events, states, conditions - whether they exist in the real world or not. It then may or may not be a property of such entities that they exist in the real world. In the sentence ( l ) John worships Zeus, the worshipping event and John, but not Zeus, exist in the real world, but all three exist in the (overpopulated) Platonic univeto. Similarly, in John wants to fly.</Paragraph> <Paragraph position="10"> John's flying exists in the Platonic universe but not in the real world.l&quot; The logical notation then is just first-order predicate calculus, where the universe of discourse is a rich set of individuals, which are real, possible auad even impossible objects, events, conditions, eventualities, and so on.</Paragraph> <Paragraph position="11"> Existence and truth in the actual universe are treated as predications about individuals in the Platonic universe. For this purpose, we use a predicate Ezist. The formula Ezist(JOllN) says that the individual in the Platonic universe denoted by JOHN exists in the actual universe, s The formula (2) Ezist{g) ^ run'(E, JOHN) says that the condition E of John's r~mning exists in the actual universe, or more simply that &quot;John rains&quot; is true, or still more simply, that John runs. A shorter way to write it is run( JO lf N).</Paragraph> <Paragraph position="12"> Although for a simple sentence like &quot;John rmls ~, a logical form like (2) seems a bit overblown, when we rome to real sentences in English discourse with their variety of tenses, modalities and adverbial modifiers, the more elaborated logical form is necessary. Adopting the notation of (2) has Hw eth,ct of splitting a sentence into its propositional content - run'(L', JOHN) and its assertional claim - gzist(E). This frequently turns out to be useful, as the latter is often in doubt until substantial work has been done by discourse interpretation processes. An entire sentence may be embedded within aa indirect proof or other extended counts{factual.</Paragraph> <Paragraph position="13"> We are now in a position to state formally the systematic relation between the unprimed and primed prrtlicat~ as an axiom schema. For every n-sty predicate p, (Vet ..... z,i)p( zl ..... z,i) ~ (3e) Ezi,,t(e)Ap'(e, zt ..... z,i) That is, if p is true of zl ..... z,s, then there is a condition e of p's being true of zt, ..., z~, amd ~ exists. Conversely, (re, zl ..... z,,)gzist(e) A p'(e, z, ..... z,,) ~ p(z, ..... z,,) Thai is. if * is the condition of p's being tnle of zt ..... Jr,,, and e exists, then p is true of =,,..., z,,. We can compress these axiom schemas into one formula: {'31 (Vii ..... Zei)p(,,Z'l ..... Z,l) --= (3elgzist(e)A p'(e.,z I ..... z,,i) A sentence in English asserts the existence of one or more eventualities in the real world, and this may or may not imply the existence of other individuals. The logical form of sentence the logical form of &quot;John wants to fly&quot; is IOns need not adhere to Platonism to accept the Platonic universe. It ran be viewed a~ t socially constituted, or conventional, con.true:ion, which is never~hele~ highly constrained by :he way the (not directly accessible} material world is. The degree of constraint is variable. We are more constrained by the miteriaJ world to belie~ in trees and chairs, le~ so to believe in patriotism or ghosts.</Paragraph> <Paragraph position="14"> iThe re~der might chaos# to think ot&quot; the Platonic universe u the univenm of pmmibln individuals, although 1 do not want to exclude Io~eallll impossible individua/s, such - the condition John helio~ to exist when he</Paragraph> <Paragraph position="16"> This implies Ezist{JOHN) but not Ezist(EI). When the existence of the condition corresponding to some predication implies the existence of one of the arguments of the predication, we will say that the predicate is transparent in that argument, and opaque otherwise, i Thus, worship and want are transparent in their first arguments and opaque in their secottd arguments. In general if a predicate p is transparent in its nth argument z, this can be encoded by the axiom (re ..... =, ...)p'(e ..... =, ...) ^ Ezi~t(e) ~ Ezist(z) s That is, if e is p's being true of z and e exists, then z exists.</Paragraph> <Paragraph position="17"> Equivalently, (V..., x, ...)p( .... z, ...) 3 E.'zist(.~) In the absence of such axioms, predicates are a.ssltmed to be opaqne.</Paragraph> <Paragraph position="18"> The following sentellce illustrates the exleHt Ii) ~'hich we must have a way of eel)resenting existent and llOlle',~i',l~'tlt ',i;iles and events ill ordinary discourse.</Paragraph> <Paragraph position="19"> ('l) &quot;rhe government has repealedly refused to deny Ihat Prime Minister Margaret Thatcher vetoed the ( :hannel Tutmel at her summit meeting with President Mitterand on 18 May, as Ne~s Scientist revealed last week. ~ In addition to tlw ordinary individuals Margaret Thatcher anti President Mitterand anti the corporals entity ,Ve., ,b'ezenliM. there are the int,.coals of time IX May and &quot;la:-,i' week', the a.s yet llOlleNi',ll'nt Chilly. l.he ( 'hannrl &quot;l',miwl, an in,Ii+idlial revealing ew'llt and the complex cw.nt ,~f lhc ,~Jllnli{il meeting, which actually oecllrred, a set of real refu.~als (listrihuled acr{)~s time in a l)articular way, a denial event whieil did not occur, and a vetoing event whh'h may or may {lot have occurred.</Paragraph> <Paragraph position="20"> Let us lake P,ist{/fs) to mean that Ea existed in the pant and Perfect{E,) to mean what the peril'el lense means, m*l~hly.</Paragraph> <Paragraph position="21"> that /re existed in Ihe pa.st and may sol .Vcl be c.mph.ted. The representation of just Ihe verb, nomin;tlizali.ns, adw.rhials and tenses of senienee ('11 is x4 fiAlow~: I' er feet( F:; ) A repe,tte,ll I'.'l ) A r,&quot; f lt.4e'( I.'l , ( ;( ) l&quot;l'. 1&quot;;:) A den!ldeg( I'::, (;()UT. Ha) A .rio'( I'.'a, AI7&quot;. ('7&quot;) A at'(E.. E~. ;';..) A racer'(If;. ,~.17&quot;. l'3f) Anti{ F.'s. 18AI -I I&quot; )A Past( b;~ )Area,col'( Ira. , v.~,', E.~) A last- e,eck( bfa ) Of lhe vario.s enliti{-~ real'reed In. Slit&quot; 4cnleliee. via .sprained predicate4, a.sseris lhe t.xisilonel , of a lypir;tl reflisal \['it ill ,1. &quot;~el of reilisals and Ihe rt.vrlaiion /'.',~. 'l'hl. r\i-i,.nc,. ,,f lit,, rq,flisal implies the exi.~lclieC {,f Ihe ~ovi'rilllll'lll h ,t,>,'- il,,i illil;l~ the eXislenee {~f the dcllial; quile Ihe ,llllll,~li,' h iii;i)' ~llt.*.C/t,-I {hi' egi~i.ellel. +if the vein. |lut ccrlainl) d{.'., lllll imply il. TI., r~'~elalion /fa, liowever, implies the existence of both the Nero Scientist 4Mere properly, we shnuld say &quot;,'sist~ntially transparent&quot; ~n,t &quot;exlsten. tinily opaque', since this notion does not coincide exactly with re/'eremtia/ /renSl~lrenci,.</Paragraph> <Paragraph position="22"> SQuantification in this notation in always ow-r entili,.s in the Platonic universe. F, xistenee in the reid world is ,'apress~.d by predicate.s, in particular the predicate gzisi.</Paragraph> <Paragraph position="23"> s'rhis sentence is taken from the Nea, Scientist, June 3. 1962 {p. 6321. \[ am indebted to Paul Martin fur calling it to lily &ttentl,~n, NS and the at relation E4, which in turn implies the existence of the veto and the meeting. These then imply the existence of Margaret Thatcher MT and President Mitterand PM, but not the Channel Tunnel CT. Of course, we know about the existence of some of these entities, such ms Margaret Thatcher and President Mitterand, for reasons other than the transparency of predicates.</Paragraph> <Paragraph position="24"> Sentence (4) shows that virtually anything can be embedded in a higher predication. This is the reason, in the logical notstins, for flattening everything into predications about individuMs. null There are four serious problems that must be dealt with if this approach is to work - quantifiers, opaque adverbials, the distinction between de re and de ditto readings of belief reports, and the problem of identity in intensional contexts.</Paragraph> <Paragraph position="25"> I have described a solution to the quantifier problem elsewhere (Hobbs, 1983). Briefly, universally quantified variables are reified ms typical elements of sets, existential quantification inside the scope of universally quantified variables are handled by means of dependency functions, and the quantifier structure of sentences is encoded in indices on predicates. In this paper i will address only the other three problems in detail.</Paragraph> </Section> <Section position="5" start_page="83" end_page="83" type="metho"> <SectionTitle> 3 Opaque Adverbials </SectionTitle> <Paragraph position="0"> \[t seems reasonably natural to treat transparent adverbials as properties of events. For opaque adverbials, like &quot;almost&quot;, it seems lees natural, and one is inclined to follow Reichenbach (1947} in treating them ms ftmctionais mapping predicates into predicates. Thus, John is almost a man.</Paragraph> <Paragraph position="1"> would he represented almo,t( man )( J ) That is, almos~ maps the predicate man into the predicate &quot;almost a man', which is then applied to John. This representation is undesirable for our purposes since it is not first-order. It would be preferable to treat opaque operators as we do transparent ones, ms properties of events or conditions. The sentence would be represented almost(E) A manl( E, J) But does this get as into dil~cuity? First note that this representation does not imply that John is a man, for we have not asserted g's existence in the real world, and almo,t is opaque and does not imply its argument's existence.</Paragraph> <Paragraph position="2"> But is there enough information in E to allow one to determine the truth value of aimomt(E) in isolation; without appeal to other facts? The answer is that there could he. We can construct a model i~ which for every functional F there is a corresponding equivalent predicate q, such that (vp, ~(F(p)(z) -- (-3s)q(~) ^ p'(e, :)) The existence of the model shows that this condition is not necessarily contradictory.</Paragraph> <Paragraph position="3"> Let the ,miverse of discourse D be the class of finite sets built out of a finite set of urelements. The interpretation of a constant X will be some element of D; call it I(X). The interpretation of s monsdic predicate p will a subset of D; call it lip). Then if E is such that p'(E, X), we define the interpretation of E to be < l(p), \[(X) >.</Paragraph> <Paragraph position="4"> Now suppose we have a functional F mapping predicates into predicates. We can define the corresponding predicate q to be such that q(E) is true iff there are a predicate p and a constant X where the interpretation of E is < I(p), \[(X) > and F(p)(X) is true.</Paragraph> <Paragraph position="5"> The fact that we can define such a predicate q in a moderately rich model means that we are licensed to treat opaque adverbials as properties of events and conditions.</Paragraph> <Paragraph position="6"> The purpose of this exercise is only to show the viability of the approach. I am not claiming that a running event *8 an ordered pair of the runner and the .set of all runners, although it should he harmless enough for those irredeemably committed to set-theoretic semantics to view it like that.</Paragraph> <Paragraph position="7"> It should be noted that this treatment of adverbials has consequences for the individuating criteria on eventualities. We can say &quot;John is almost a man ~ without wishing to imply &quot;John is almost a mammal,&quot; so we would not want to say that John's being a man is the same condition as his being a mammal. We are forced, though not unwillingly, into a position of individuating eventualities ,,,'cording to very fine-grained criteria.</Paragraph> </Section> <Section position="6" start_page="83" end_page="85" type="metho"> <SectionTitle> 4 De Re and De Dicto Belief Reports </SectionTitle> <Paragraph position="0"> The next problem concerns the distinction (due to Quine (19.56)) between de re and de ditto belief reports. A belief report like (5) John believes a man at the next table is a spy.</Paragraph> <Paragraph position="1"> has two interpretations. The de dieto interpretation is likely in the circumstmace in which John and some man are at adjacent tables and John observes suspicious behavior. The de re inter.</Paragraph> <Paragraph position="2"> pretation is likely if some man is sitting at the table next to the speaker of the sentence, and John is nowhere around but knows the man otherwise and suspects him to be a spy. A sentence that very nearly forces the de re reading is John believes Bill's mistress is Bill's wife/ whereas the sentence John believes Russian consulate employees are spies.</Paragraph> <Paragraph position="3"> strongly indicates a de ditto reading. In the tie re reading of (5), John is not necessarily taken to know that the man is in fact at the next table, but he is normally a.ssumed to be able to identify the man somehow. More on ~identil'y&quot; below. In the de divan reading John believes there is a man who is both at the next table and t spy, but may be otherwise unable to identify the man. The de re reading of (5) is usually taken to support the inference (6) There is someone John believes to be a spy.</Paragraph> <Paragraph position="4"> whereas the de ditto reading supports the weaker inference (7) John believes that someone is a spy.</Paragraph> <Paragraph position="5"> YThi- ,~x&quot;~mple is due to Moore and Hendrix (1982).</Paragraph> <Paragraph position="6"> As Quine has pointed out, as usually interpreted, the first of these sentences is false for most of us, the second one true. A common notational maneuver (though one that Quine rejects) is to represent this distinction as a scope ambigafity. Sentence (6) is encoded as (8) and (7) as (9): (8) (~z)believe(J, spy(z)) (9) believe(J, (3z)spy(z)) If one adopts this notation and stipulates what the expressions mean, then there are certainly distinct ways of representing the two sentences. But the interpretation of the two expressions is not obvious. It is not obvious for example that (8) could not cover the case where there is an individual such that John believes him to be a spy but has never seen him and knows absolutely nothing else about him - not his name, nor his appearance, nor his location at any point in time - beyond the fact that he is a spy.</Paragraph> <Paragraph position="7"> In fact. the notation we propose takes (8) to be the most neutral representation. Since quantification is over entities in the Platonic universe, (8) says that there is some entity in the Platonic universe such that John believes of that. entity that it is a spy. Expression (8) commits us to no other beliefs on the part of .John. When understood in this way, expression (8) is a representation of what is conveyed in a de ditto belief report. Translated into the flat notation and introducing a constant for the existentially quantified variable. (8) becomes (10) believe{J. P) A spy'(P.S) Anything else that John believes about this entity must be stated explicitly. In particular, the de dieto reading of (5) would be represented by something like (11) believe(J, P) A spy'(P, S) A believe( J, Q) A at'(Q, S, T) where T is the next table. That is, John believes that S is a spy and that .q is at the next table. John may know many other propcriies about S and still fall short of knowing ,rho the spy is. There is a range of possibilities for John's knowledge, from the bare statements of (lO) and (It) that correspond to a ,le ditto reading to the full-blown knowledge of S's hh'ntity that is normally present in a de re reading. In fact, an FBI agent would progress through just such a range of belief states on his way to identifying the spy.</Paragraph> <Paragraph position="8"> To state John's knowledge of S's identity properly, we wo*tld have to state explicitly John's belief in a potentially very large collection of properties of the spy. To arrive at a succinct way of representing knowledge of identity in our notation, let us con. sider the two pairs of equivalent sentences: What is that? Identify that.</Paragraph> <Paragraph position="9"> The FBI doesn't know who the spy is.</Paragraph> <Paragraph position="10"> The FBI doesn't know the spy's identity.</Paragraph> <Paragraph position="11"> The answer to the question &quot;Who are you?&quot; and what is required before we can say that we know who someone is or that we know their identity is a highly context-dependent matter. Several years ago, before I had ever seen Kripke, if someone had asked me whether I knew who Saul Kripke was, I would have said, ~Yes. tle's the author of Naming and Neeessd~. ~ Then once ! was at a workshop which I knew was being attended by Kripke, but I didn't yet know what he looked like. If someone had asked me whether I knew who Kripke was, I would have had to say, &quot;No. * The relevant property in that context, was not, his authorship of some paper, but any property that distinguished him from the others present, such as &quot;the malt in the back row holding a cup of coffee*.</Paragraph> <Paragraph position="12"> Knowledge of a person's identity is then a matter of knowing some context-dependent essential property that serves to identify that person for present purposes - that is, a matter of knowing who he or she is.</Paragraph> <Paragraph position="13"> Therefore, we need a kind of place-holder predicate to stand for this essential property, that in any particular context can be specified more precisely. It happens that English has a morpheme that serves just this function - the morplwme &quot;wh&quot; Let us then posit a predicate u,h that stands for the contextually ,tetermined property or conjunction of properfes that wotild coiult as an identification in that particular context.</Paragraph> <Paragraph position="14"> The de re reading of (5) is generally taken to include John's knowledge of the identity of the alh'd~cd spy. Assuming this, a de re belief report would be represented a.s a conjunction of two beliefs, one for the main predication and the other expressing knowledge of the es~,,ntial properly. Ihe what-oess, of the arg~sment of the predication.</Paragraph> <Paragraph position="15"> believe{J. 1)) A spv'(l'. X) A kno.,( I. c~) A u,h'(~.~, X) That is. John believes .~,' is a ~py and .Iohn kn.w'~ who .~,' i-Ilowever. let us probe this ,li~Iinct&quot;m j~lsI a lit th. more deeply and in particular call into qtlt,~,!loll whether knowh'd~e of identity is really part of the meanmg of the sentence in the de re reading. The representation of the de ditto reading of 3. \[ have said. is (12) believe(J, P) A spy'(P, S) A behei,e(J.Q) A ,it'(Q, S,T) Let its represent the de re rea(lin~ a.,~ { 13a) believe( ./. l'} A .'I'Y'( l'. ,'; ) A /.'st ~t( C~ ) A ,H'( t~..~'. 7') (131)) A kt, ou,( J. I:1A u.h'( It'..',') What is common to(121 and (l::) arc flit. crltijiinci,, hel:,~','( /. P). spy'(/'. S) and at'(Q..s'. 7&quot;). &quot;\['hcre is a !.;viiuiiu. ainhi!.,.uii.v a..~ to whelher Q exists in the real world (de re I (Ir i~ mcrely Iwlieved by John (de dicto), lu addition. (I::) incl.de, the conjuncts tnolt,(J. R) and ,vh'(/L.s') - lint. (i:>>i~i.</Paragraph> <Paragraph position="16"> t'~llt are these necessarily part of the ,le re illfl,rllrelalh,ii ~'Jf sentence 5? Th, followin~ t.xanillle cast', d(.ihl .. thi. S.i)l)~,s~, the entire ffotary ('.hill i~ seall.d ;ll ilia. l:ihh, ill,\i I,i llw -p~'al.ct of ~i. I;ilt John'doesn'i kllOl ihi-. ,h)hli t..Ih.~ v- Ih;ll -,,lili, llit, lilher of Ihe Rolary f'hih is ~i -ll). hilt ha- ll~ I,l~'a which one .Sefllence 5 describes tflis ~.ilUail~ln. ;lli~l i)iily I I:;al h.ld~, not (13hi and not (12). Jlult'ment,; are sonil'iiml&quot;~ linci'rlaill ~K4 to whether sentence 5 is appropriatc in these circllms/ances, but it is certain that the sentence John believes someone at the next table is a spy.</Paragraph> <Paragraph position="17"> is appropriate, and that is sufficient for the argument.</Paragraph> <Paragraph position="18"> It seems then that the toni,nets know(J. R) and ~,h'(R.S) are not part of &quot;#hat we want in the initial logical form of the sentence, s but only a very common conversational implicature. The reason the implicature is very. common is that if iAnother way of putting it: they are not part. of the literal meaning of the sentenc;e.</Paragraph> <Paragraph position="19"> John doesn't know that the man is at the next table, there must be some other description under which John is familiar with the man. The story I just told provides such a description, but not one sufficient for identifying the man.</Paragraph> <Paragraph position="20"> This analysis is attractive since it allows us to view the de re de dicto distinction problem u just one instance of a much more general problem, namely, the existential status of the grammatically subordinated material in sentences. Generally, such material takes on the tense of the sentence. Thus, in The boy built the boat.</Paragraph> <Paragraph position="21"> a building event by z of y takes place in the past, and we assume that a was a boy in the past, at the time of the building. But in Many rich men studied computer science in college.</Paragraph> <Paragraph position="22"> the most natural reading is not that the men were rich when they were studying computer science but that they are rich now. In The flower is artificial.</Paragraph> <Paragraph position="23"> there is an entity z which is described as a flower, and z exists, but its &quot;flower-hess&quot; does not exist in the real world. Rather, it is a condition which is embedded in the opaque predicate &quot;artificial'.</Paragraph> <Paragraph position="24"> It was stated above that the representation (10) for the de ditto reading conveys no properties of S other than that John believes him to be a spy. In particular, it does not convey S's existence in the real world. S thus refers to a possible individual, who may turn out to be ,wtual if, for example, John ever comes to be able to identify the person whom he believes to be the spy, or if there is some actual spy who has given John good cause for his suspicions.</Paragraph> <Paragraph position="25"> However, S may not be actual, only possible. Suppose this is the case. One common objection to possible individuals is that they may seem to violate the Law of the Excluded Middle. Is S married or not married? Our intuition is that the question is inappropriate, and indeed the answer given in our formalism has this flavor. By axiom (3), married(S) is really just an abbreviation for married'( g, S) ^ gzist(E). This is false, for the existence of E in the real world would imply the existence of S. So married(S) is also false. But its falsity has nothing to do with S's marital status, only his existential status. The predication unmarried(S) is false for the same reason. The primed predicates are basic, and for them the problem of the excluded middle does not arise. The predication maeried'(E, S) is true or false depending on whether E is the condition of S's being married. An unprimed, trmxsparent predicate carries along with it the existence of its arguments, and it can fail to be true of an entity either through the entity being actual but not having that property or through the nonexistence of the entity.</Paragraph> </Section> <Section position="7" start_page="85" end_page="86" type="metho"> <SectionTitle> 5 Identity in Belief Contexts </SectionTitle> <Paragraph position="0"> The final problem I will consider arises in de dieto belief reports.</Paragraph> <Paragraph position="1"> It is the problem of identity in intensional contexts, raised by grege (1892). One way of stating the problem is this. Why is it that if (14) John believes the Evening Star is rising. and if the Evening Star is identical to the Morning Star, it is not necessarily true that (15) John believes the Morning Star is rising.</Paragraph> <Paragraph position="2"> By Leibniz's Law, we ought to be able to substitute for an entity any entity that is identical to it.</Paragraph> <Paragraph position="3"> This puzzle survives translation into the logical notation, if John knows of the existence of the Morning Star and if proper names are unique. The representation for (the de dicto reading of) sentence (14) is From all of this we can infer that the Morning Star M,q is also an Evening Star and hence is identical to ES;, and hence can be substituted into ri.se'(Pi, E.S') to give rise'(PI, MS). Then we have believe( J, P, ) A vine'( P,, M S ) A believe( J, Q: ) AMorning-b'tar'(Q:, MS) This is a representation for tile paradoxical sentence (15). There are three possibilities for dealing with this proi)lem. The first is to discard or restrict I,eibniz's Law. The second is to deny that the Evening ~tar and the Morning Star are identical a.s entities in the Platonic universe; they only happen to he identical in the real world, and that is not sullieient for intersubstitutivity The third is to deny that expression (16) represents ~entence (14) because &quot;the Evening Star&quot; in (14) does not refer to what it seems to refer to.</Paragraph> <Paragraph position="4"> The first possibility is the approach of researchers who treat belief as an operator rather than as a predicate, and then re. strict substitution inside the operator. ~ We cannot avail ourselves of this. solution bec.ause of the flatness of our notation. The predicate rtse is surely referentially transparent, so if ES and MS are identical, M,S&quot; can he substituted for E:S in the expression rine'(l'l,Eb') to give rtse'(l'\].M.S'). Then the expression belier,e( J, I'1) wouhl not even require substitution to he a belief about the Morning Star.</Paragraph> <Paragraph position="5"> In any case, this approach does not seem wise in view of the central importance played ia discourse interpretation by the identity of differently presented entities, i.e. by coreference. Free intersubstitutibility of identicals seems a desirable property to preser'se.</Paragraph> <Paragraph position="6"> The second possible answer to Frege's problem is to say that in the Platonic universe, the Morning Star and the Evening Star *This ia a purely syntactic approach, and whPn one tries to construct * semantics for it, one is generally driven to the third possibility. are different entities. It just happens chu in the res/world they are idemical. But it is not true that E$ = MS, for equality, like quantification, is over entities in the Platonic universe. The fact that E,.~ and MS ate identical in the real wodd (call this relation rw-identicai) must be stated explicitly, say, by the expression For reuonin~ shout &quot;r~-idmtical&quot; entities, thm~ is, Platonic entities th~ mrs identical in the real world, we may cake the fol-Iowin~ approach- Substitution in re(erenmdly trsmsparent contexts wonld be ,z:hieved by ~so o( the sx/om schema (17) (Vel, es. e4 .... )p/(et ..... C/s .... ) A rw.idsnticed(e4, eS) D (::leZ)p~(ez ..... e4, ...) A r~n.4dsnfica~(ez, e! ) where es is the /cth argument of p sad p is referentially cras~, parent in im kth ar~ment. That is, if et is p's being true of {S ~ e$ ~ e4 SA'~ identical in the real world, then there is a condition C/z o(p's bein~ true of e4, ~ ez is identical to e~ in the real worid. Substitution o/' h'w.identicab&quot; in s condition resulra not in the same condition but in ,n &quot;rw-identical&quot; condition. Them would be such an sx/om for the ~C/ u.gument o( bei*eve but not for its referentially opaque second srlrumeut.</Paragraph> <Paragraph position="7"> A.z/ome will express the fact that r,~.idzntiea~ is an equlvs. lence relation: (~z)r~u-idsnticat( z, ~t) (~=, v )~w.identieal( =, V) D e~.4dentie~(v, z) ('V=, ~, s)r~.4denticai( z, ~) A re.identical(V, s) m ,.-id,,,tie=/(z, ,) Finally, cl~ followins Lziom, co.her with Lziom (17), wou/d exprem L~ibnis's L,w: (Ve~, e~)r,,,-identica(s,, q) ~ (~,t(s,) s ~=ist(s~)) From all of (hi, we can prove that if the gVenin~ Star then the Momin~ Star rises, but we clmsot prove from John's belief chat the Evening Star rim that John believes the Morning Star rises. If John knows the MornlnC/ Star sad the Evening Star are identical, sad he knows ,xiom (17), then his belief that eke MoruinC/ $~m' rim can be proved u one would prove belief in the consequences of ~y o*h~ syilot~m whose premises he believed, in accordance with * m.*s~ment of resmmnC/ shout belief developed in * Iont~.,r vere/on o( th/s pal.ee.</Paragraph> <Paragraph position="8"> This solution is in the spirit of our whole representational ~p. preach in ch*~ it forces tm co be paln(ully expticit about every. chm~. The notation does no magic for us. There is a sit, nificant cost a~.socis:ed with th~s solution, however. When proper names * re represented u predicates sad not u constants, the natural way co state the uniqueness o( proper names is by mesas o( axioms of the foiiowinC/ sort: (~=, y)Euen,ng*~tar(z) A &quot;~uensng-Star(g) D Z I y BUt since from ~he sX/oms for r~-identieai we can show chat &quot;~veninf-~tar(~fS), it would follow chsc M~ = ~S. We mnst thus restate the axiom for \[he umqueness o( proper uames a=</Paragraph> <Paragraph position="10"> A similar modification mus, be made for functions. Since we are using only predicates, the uniqueness of the value of a function must be encoded with an axiom like (Y==, V, :)father(=, z) ^ father{v, z) ~ = = y If = and y are both fathem o/&quot; z, {hen z and y are the same. This wonld have to be replaced by the axiom (V=, y, z ) father( =, :)^father(y, z) 3 rw-identicai( =, V) The very common problems involving ressomn K shout equality, which can be done elRciently, are thus translated into problems involvinf resmnm~ shout the predicate re.identical, which is very cumbersome.</Paragraph> <Paragraph position="11"> One way to view Ch/s second solution is ~ a l~x co the first solucian. For &quot;=*&quot; we substitute the relation r~;-qden~,cad, ~md by means of axiom schema (17), we force substitutions co propagate to the eventualities they occur in, and we force the distinction between referentially transparent and referentially opaque predicates to be made explicitly. It is thus an indirect way of rejecting L,eibnis' Law.</Paragraph> <Paragraph position="12"> The third solution is to say that &quot;the Eveninf Star* in sentents (14) does not really refer to the Evening Star, but co some abstract entity somehow related to the Evenin~ Star. That is.</Paragraph> <Paragraph position="13"> sentence (14) is re-fly en example of metonymy. This may seem counterintuitive, sad even bizarre, at first blush. But in fact the most widely *,'espied clmmical solutions to the problem of identiw ate of thn, flavor. Foe Fre~e (1892) &quot;the Evening Star ~ in sentence (14) does no* refer co the Evenin~ Star but co the tenme of the phrsac &quot;the Evening Star ~. \[n a more recent approar.h, Zalta (1983) ts~es such noun phrases co refer co &quot;abstrict objects&quot; related to the resJ object. In both approaches noun phrues in intemional context~ refer co senses or abstract objects, while other noun phrues refer co actual entities, sad so it is necessary co specify which predicates are intensioa*,l. \[n a Manta{avian approach, &quot;the Evening Star&quot; would be taken to refer co the inter.on o( the Evening Star, not its e=te~*on in the real world, sad noun phrases would al,vays be taken co refer co intensions, -Ithough for nonintensional predicates there would be mesmng postulates chat make this equivalent co reference co extensions.</Paragraph> <Paragraph position="14"> Thus, in all these approaches intentional and extensional predicates must be distintmished explicitly, sad noun phrs~s in intensional contexts are systematically interpreted metonymically. It would be em,y enouch in our framework co implement these q3proaches. We c,m define a function a o( three arguments - the actual entity, the co,niter, sad the condition used co describe the entity - chat returns the sense, or intention, or abstract entity, corresponding co the ~ctual entity for chat C/ognizer ~nd that condition. Sentence (14) would be represented, not ~ (16).</Paragraph> <Paragraph position="15"> but u (18) betievse(d, Pt) ^ rise~(Pt,a(E S, d, Ql)) ^ beiieve(J, Qt) AEusninf.StaC/(Qc, F,S) l tend r.o prefer co cl~nk o( the vaJue o( a(ES, J, Qt ) as sa abstract entity. Whatever it is, it is necessary chat the vMue of a(E2, J, Qs) be something different from the value of a( ES, J. Q~.) where Movninq-StarJ(Q:, ES). That is. different ~tr'act objects must correspond co the condition QI of being the Evening Star and the coaditioo Q: o( being the Morning Star. It is because o( this feature ~hat we escape the problem o( intenmbstitutivity of identieakt, fur substitution o( MS for ES in (18) yields &quot;...Ariee/(Pt,a(MS, J, Q1))A...&quot; rather than &quot;...Ariee~(Pl,,~(M$, J,Q=)) A...', which would be the representation of sentence (15).</Paragraph> <Paragraph position="16"> The dif~culty with this approach is that it makes the interpeeration o/&quot; noun phrases dependent on their embedding context: \[ntensionai context -* meC/onymlc interpretation Extensional context -- noumetonymic interpretation It thus violates, though not soriousiy, the nmve com~tionaiity that \[ have been at so many pehm to preserve. Metonymy is a very common phenomenon in discourse, but l prefer to think o( it as occurring irregularly, sad not 8a siKnalled systematieafly by other elemenu, in the sentence.</Paragraph> <Paragraph position="17"> Having laid out the three possible solutious and their sho~-C/ominKs, \[ find tha~ \[ would like to avoid the problem o/&quot; identity altogether. The third sppro.-'h suggests a ruse for doing so. We can amume tha~, in general, (16) is the representation of sentence (14). We invoke no extra complications where we don't have to. When, in interpreting the text, we encounter a difficulty resulting from the problem o/' identity, we can go back and revise our in~rprocatmn o((14), by mmuming the reference rmmt have been a metonymie one to the sbstr-,'t entity and not to the actual entity. In theee cm it would be ts if we m'e saying, &quot;John couldn't believe about the Evening Star itself that it is rising. The par'edox shows that he is insufficiently acquamted with the Evening Star to refer to it ~metly. He must be talking about an abetr~t entity rotated to the Rvenmg Star.&quot; My ~less is the, we will not have to resort to thin run often, for \[ suapect the problem rarely srmes in acmad dim:ouume interpre~ion.</Paragraph> </Section> <Section position="8" start_page="86" end_page="86" type="metho"> <SectionTitle> 6 The tLole of Semantics </SectionTitle> <Paragraph position="0"> Let me cla~ by making some commenm about ways of doing semantics. Semangcs is the =temp~.d specification of the re-In, ion between language and C/he world. However, this requires a theory of the world. There is a ,peetrtun of choices one can make in this retard. At one end o/' the spectrum - l~'s say the right end - one can *,/opt the &quot;coreeet&quot; theory of the wodd, the theory Oven by quantum mechsmcs u~/ the other sciences. If or=. doe= this, .emantics become= impmmbte because it is no lem than Ill of sr../e~m, a fset that has led Fodur (1980) to exp~ some deapmr. Thor's mo much o( a m/smasch between the way we view the wodd and the way che wodd reaily is. At ~he left end, oue can mmume a theory o( the w~dd that is isomorphic to the way we caik -hour it. Whmt \[ have been doing in this paper, in fact, is an effort to work out the deem ~- in such = theory. In this cue. semantics becomes very neudy trivial Meet activity in ~emmtics today is slightly to toe ,~t of the extreme left end of this spectrum. One makes certam smumptious about the nature of the wodd that timely mflt~t 18nKumle, and doesn't make certain other alumptions. Where one h .= fa~ed to m -~,. the neceeac~, aesumpoons, pusaies app~w, tnd semanr~iC/~ becomes an effort to soive those puzzles. Neve~heiess, it fsils to move far enough away from langms~e to re, reseat d~nifieant pt~gre~ cows~t the tight end of the sl~.etrum. The pmition \[ advocate is that there is no remmn to make our task mo~ difficult. We wdl have pus~des enough to mlve when we get m diseourae.</Paragraph> <Paragraph position="1"> A,~o~i~t~smnm l bavo profited from distmmions about this work with Chris Menze/, Bob Moore, Start Rosen~hein, and Ed Zaita. This research wu suppor~'d by NIH Grant LM03611 from the National Library o/&quot; Medicine, by Grant IST-8209346 from the Na~ionai Science Founds*ion, and by a gift from ~he Systems Developwent Foundation.</Paragraph> </Section> class="xml-element"></Paper>